{
 "cells": [
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   "source": [
    "# **Ordinary Differential Equation Solving**\n",
    "\n",
    "Author : Rakshit Kr. Singh : [Website](https://blog.greatrsingh.in/) : [LinkedIn](https://www.linkedin.com/in/rakshit-singh-ai/) : [GitHub](https://github.com/GreatRSingh)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ordinary Differential Equations (ODEs) are a cornerstone of mathematical modeling, essential for understanding dynamic systems in scientific and engineering fields.\n",
    "\n",
    "This tutorial aims to introduce you to ODE solving tools in DeepChem."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## What are Ordinary Differential Equations?\n",
    "\n",
    "An ordinary differential equation (ODE) is a type of differential equation that depends on a single independent variable. In contrast to partial differential equations (PDEs), which involve multiple independent variables, ODEs focus on relationships where changes occur with respect to just one variable. The term \"ordinary\" distinguishes these equations from stochastic differential equations (SDEs), which incorporate random processes.\n",
    "\n",
    "ODEs consist of unknown functions and their derivatives, establishing relationships that describe how a quantity changes over time or space. These equations are fundamental in expressing the dynamics of systems."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### General  Form of an ODE -\n",
    "\n",
    "$$\\frac{dy}{dx} = f(x,y)$$\n",
    "\n",
    "Here,\n",
    "$dy/dx$ is the derivative of $y$ with regards to $x$, and $f(x,y)$ is a function of $x$ and $y$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Why we should Care About Ordinary Differential Equations\n",
    "\n",
    "They are essential because they model how physical quantities change over time. ODEs are used in:\n",
    "\n",
    "- Physics: To describe the motion of particles, the evolution of wave functions, and more.\n",
    "\n",
    "- Engineering: To design control systems, signal processing, and electrical circuits.\n",
    "\n",
    "- Biology: To model population dynamics, the spread of diseases, and biological processes.\n",
    "\n",
    "- Economics: To analyze growth models, market equilibrium, and financial systems.\n",
    "\n",
    "- Control Systems and Robotics: In control systems and robotics, ODEs are fundamental in describing the dynamics of systems."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Solving Ordinary Differential Equations\n",
    "\n",
    "Steps:\n",
    "- Formulate the ODE: \n",
    "An ODE involves an unknown function $y(x)$ and its derivatives.\n",
    "\n",
    "$$Example: \\frac{dy}{dx} + y = e^{x}$$\n",
    "\n",
    "- Find the general solution:\n",
    "The goal is to find the function $y(x)$ that satisfies the ODE. This process often involves integration.\n",
    "\n",
    "- Apply initial or boundary condition: To find a specific solution, you often need additional information, such as the value of the function and its derivatives at certain points. These are called initial or boundary conditions.\n",
    "\n",
    "## Methods for Solving ODEs in DeepChem\n",
    "\n",
    "DeepChem boasts a number of methods for solving ODEs. Some of them are:\n",
    "\n",
    "- Euler's Method\n",
    "- Mid Point Method\n",
    "- 3/8 Method\n",
    "- RK-4 Method"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Euler's Method (1st Order Runge-Kutta Method)\n",
    "\n",
    "- It is the simplest Runge–Kutta method\n",
    "- Explicit Runge–Kutta method with one stage\n",
    "\n",
    "$$y_{n+1}=y_{n}+hf(t_{n},y_{n})$$\n",
    "\n",
    "\n",
    "#### Mid-Point Method (2nd Order Runge-Kutta Method)\n",
    "\n",
    "- It is also called modified Euler's method\n",
    "- second-order method with two stages\n",
    "\n",
    "$$y_{n+1}=y_{n}+hf\\left(t_{n}+{\\frac {1}{2}}h,y_{n}+{\\frac {1}{2}}hf(t_{n},\\ y_{n})\\right)$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "import warnings\n",
    "warnings.filterwarnings(\"ignore\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from deepchem.utils.differentiation_utils.integrate.explicit_rk import mid_point_ivp, fwd_euler_ivp\n",
    "import matplotlib.pyplot as plt\n",
    "import torch\n",
    "\n",
    "# Simple ODE dy/dt = a*y\n",
    "def ode(t, y, params):\n",
    "    a = params[0]\n",
    "    return y * a\n",
    "\n",
    "t = torch.linspace(0, 20, 5)\n",
    "y_0 = torch.tensor([1])\n",
    "a = torch.tensor([1])\n",
    "\n",
    "sol_fwd_euler = fwd_euler_ivp(ode, y_0, t, [a])\n",
    "sol_mid_point = mid_point_ivp(ode, y_0, t, [a])\n",
    "\n",
    "plt.plot(t, sol_fwd_euler.squeeze(), \"-b\", label=\"Euler's method\")\n",
    "plt.plot(t, sol_mid_point.squeeze(), \"-r\", label=\"Mid-point method\")\n",
    "plt.legend(loc=\"upper left\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### RK4 Method\n",
    "\n",
    "$${\\displaystyle {\\begin{aligned}y_{n+1}&=y_{n}+{\\frac {h}{6}}\\left(k_{1}+2k_{2}+2k_{3}+k_{4}\\right)\\\\t_{n+1}&=t_{n}+h\\\\\\end{aligned}}}$$\n",
    "\n",
    "for n = 0, 1, 2, 3, ...\n",
    "\n",
    "$${\\displaystyle {\\begin{aligned}k_{1}&=\\ f(t_{n},y_{n})\\\\k_{2}&=\\ f\\!\\left(t_{n}+{\\frac {h}{2}},y_{n}+h{\\frac {k_{1}}{2}}\\right)\\\\k_{3}&=\\ f\\!\\left(t_{n}+{\\frac {h}{2}},y_{n}+h{\\frac {k_{2}}{2}}\\right)\\\\k_{4}&=\\ f\\!\\left(t_{n}+h,y_{n}+hk_{3}\\right)\\end{aligned}}}$$\n",
    "\n",
    "#### Second Order Differential Equation\n",
    "\n",
    "##### Example: $\\frac{d^{2}y}{dt^{2}} + \\frac{dy}{dt} - 6y = 0$\n",
    "given, $y(0) = 5$ and $dy/dt$ at t=0 is -5\n",
    "\n",
    "##### Procedure:\n",
    "$$\\frac{dy}{dt} = z$$\n",
    "$$\\frac{dz}{dt} = 6y - z$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from deepchem.utils.differentiation_utils.integrate.explicit_rk import rk4_ivp\n",
    "import matplotlib.pyplot as plt\n",
    "import torch\n",
    "\n",
    "def sode(t, y, params):\n",
    "    y, z = y\n",
    "\n",
    "    a = params[0]\n",
    "\n",
    "    dydt = z\n",
    "    dzdt = a * y - z\n",
    "\n",
    "    return torch.tensor([[dydt], [dzdt]])\n",
    "\n",
    "params = torch.tensor([6])\n",
    "t = torch.linspace(0, 1, 100)\n",
    "y0 = torch.tensor([[5], [-5]])\n",
    "sol = rk4_ivp(sode, y0, t, params)\n",
    "\n",
    "plt.plot(t, sol[:, 0])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Comparing with Particular Solution\n",
    "\n",
    "Particular Solution: $y = 2e^{2x} + 3e^{-3x}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "yy = 2 * torch.exp(2 * t) + 3 * torch.exp(-3 * t)\n",
    "\n",
    "plt.plot(t, yy, \"-b\", label=\"Known solution\")\n",
    "plt.plot(t, sol[:, 0], \"-r\", label=\"RK4 method\")\n",
    "plt.legend(loc=\"upper left\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Solving Lotka Volterra using Deepchem\n",
    "\n",
    "The Lotka–Volterra equations, also known as the Lotka–Volterra predator–prey model, are a pair of first-order nonlinear differential equations, frequently used to describe the dynamics of biological systems in which two species interact, one as a predator and the other as prey. The populations change through time according to the pair of equations:\n",
    "\n",
    "$${\\displaystyle {\\begin{aligned}{\\frac {dx}{dt}}&=\\alpha x-\\beta xy,\\\\{\\frac {dy}{dt}}&=-\\gamma y+\\delta xy,\\end{aligned}}}$$\n",
    "\n",
    "The Lotka–Volterra system of equations is an example of a Kolmogorov model, which is a more general framework that can model the dynamics of ecological systems with predator–prey interactions, competition, disease, and mutualism."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from deepchem.utils.differentiation_utils.integrate.explicit_rk import rk38_ivp\n",
    "import matplotlib.pyplot as plt\n",
    "import torch\n",
    "\n",
    "def lotka_volterra(t, y, params):\n",
    "    y1, y2 = y\n",
    "    a, b, c, d = params\n",
    "    return torch.tensor([[(a * y1 - b * y1 * y2)], [(c * y2 * y1 - d * y2)]])\n",
    "\n",
    "t = torch.linspace(0, 50, 10000)\n",
    "\n",
    "solver_param = [lotka_volterra,\n",
    "                torch.tensor([[10.], [1.]]),\n",
    "                t,\n",
    "                torch.tensor([1.1, 0.4, 0.1, 0.4])]\n",
    "\n",
    "sol_rk38 = rk38_ivp(*solver_param)\n",
    "\n",
    "plt.plot(t, sol_rk38.squeeze())\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### lotka volterra (Parammeter Estimation)\n",
    "\n",
    "Parameter Estimation is used to estimate the values of the changable parameters in the ODE. The parameters describe an underlying physical setting in such a way that their value affects the distribution of the measured data. An estimator attempts to approximate the unknown parameters using the measurements."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "\n",
    "dataset = pd.read_csv('assets/population_data.csv')\n",
    "years = torch.tensor(dataset['year'])\n",
    "fish_pop = torch.tensor(dataset['fish_hundreds'])\n",
    "bears_pop = torch.tensor(dataset['bears_hundreds'])\n",
    "\n",
    "plt.plot(fish_pop, \"-b\", label=\"Fish population\")\n",
    "plt.plot(bears_pop, \"-r\", label=\"Bear population\")\n",
    "plt.legend(loc=\"upper left\")\n",
    "plt.title(\"Population data\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization terminated successfully.\n",
      "         Current function value: 42.135759\n",
      "         Iterations: 153\n",
      "         Function evaluations: 251\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from deepchem.utils.differentiation_utils.integrate.explicit_rk import rk4_ivp\n",
    "import torch\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "\n",
    "def lotka_volterra(y, t, params):\n",
    "    y1, y2 = y\n",
    "    a, b, c, d = params\n",
    "\n",
    "    return torch.tensor([[a * y1 - b * y1 * y2], [c * y2 * y1 - d * y2]])\n",
    "\n",
    "\n",
    "def loss_function(params, years,fish_pop, bears_pop):\n",
    "\n",
    "    y0 = torch.tensor([[fish_pop[0]], [bears_pop[0]]])\n",
    "\n",
    "    t = torch.linspace(years[0], years[-1], len(years))\n",
    "\n",
    "    output = rk4_ivp(lotka_volterra, y0, t, params)\n",
    "\n",
    "    loss = 0\n",
    "\n",
    "    for i in range(len(years)):\n",
    "        data_fish = fish_pop[i]\n",
    "        model_fish = output[i,0]\n",
    "\n",
    "        data_bears = bears_pop[i]\n",
    "        model_bears = output[i,1]\n",
    "\n",
    "        res = (data_fish - model_fish)**2 + (data_bears - model_bears)**2\n",
    "\n",
    "        loss += res\n",
    "\n",
    "    return(loss)\n",
    "\n",
    "import scipy.optimize\n",
    "\n",
    "params0 = torch.tensor([1.1, .4, .1, .4])\n",
    "minimum = scipy.optimize.fmin(loss_function, params0, args=(years,fish_pop, bears_pop))\n",
    "\n",
    "\n",
    "alpha_fit = minimum[0]\n",
    "beta_fit = minimum[1]\n",
    "delta_fit = minimum[2]\n",
    "gamma_fit = minimum[3]\n",
    "\n",
    "params = torch.tensor([alpha_fit, beta_fit, delta_fit, gamma_fit])\n",
    "\n",
    "y0 = torch.tensor([[fish_pop[0]], [bears_pop[0]]])\n",
    "\n",
    "t = torch.linspace(years[0], years[-1], 1000)\n",
    "\n",
    "output = rk4_ivp(lotka_volterra, y0, t, params).squeeze()\n",
    "\n",
    "plt.plot(t, output)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## SIR Epidemiology\n",
    "\n",
    "The SIR model is one of the simplest compartmental models, and many models are derivatives of this basic form. The model consists of three compartments:\n",
    "\n",
    "- S: The number of susceptible individuals. When a susceptible and an infectious individual come into \"infectious contact\", the susceptible individual contracts the disease and transitions to the infectious compartment.\n",
    "- I: The number of infectious individuals. These are individuals who have been infected and are capable of infecting susceptible individuals.\n",
    "- R: The number of removed (and immune) or deceased individuals. These are individuals who have been infected and have either recovered from the disease and entered the removed compartment, or died. It is assumed that the number of deaths is negligible with respect to the total population. This compartment may also be called \"recovered\" or \"resistant\".\n",
    "\n",
    "$$\\frac{dS}{dt} = -\\frac{\\beta IS}{N}$$\n",
    "$$\\frac{dI}{dt} = \\frac{\\beta IS}{N} - \\gamma I$$\n",
    "$$\\frac{dR}{dt} = \\gamma I$$\n",
    "$$N = S + I + R$$\n",
    "$$R_{0} = \\frac{\\beta}{\\gamma}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import torch\n",
    "import matplotlib.pyplot as plt\n",
    "from deepchem.utils.differentiation_utils.integrate.explicit_rk import rk4_ivp\n",
    "\n",
    "def sim(t, y, params):\n",
    "    S, I, R = y\n",
    "\n",
    "    N = S + I + R\n",
    "\n",
    "    beta, gamma = params\n",
    "\n",
    "    dSdt = - beta * I * S / N\n",
    "    dIdt = beta * I * S / N - gamma * I\n",
    "    dRdt = gamma * I\n",
    "\n",
    "    return torch.tensor([[dSdt], [dIdt], [dRdt]])\n",
    "\n",
    "t = torch.linspace(0, 500, 1000)\n",
    "\n",
    "beta = 0.04\n",
    "gamma = 0.01\n",
    "\n",
    "params = torch.tensor([beta, gamma])\n",
    "\n",
    "y0 = torch.tensor([[100], [1], [0]])\n",
    "\n",
    "y = rk4_ivp(sim, y0, t, params).squeeze()\n",
    "\n",
    "plt.plot(t, y)\n",
    "plt.legend([\"Susceptible\", \"Infectious\", \"Removed\"])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## SIS Model\n",
    "\n",
    "Some infections, for example, those from the common cold and influenza, do not confer any long-lasting immunity. Such infections may give temporary resistance but do not give long-term immunity upon recovery from infection, and individuals become susceptible again.\n",
    "\n",
    "#### Model:\n",
    "$$\\frac{dS}{dt} = -\\frac{\\beta IS}{N} + \\gamma I$$\n",
    "$$\\frac{dI}{dt} = \\frac{\\beta IS}{N} - \\gamma I$$\n",
    "#### Total Population:\n",
    "$$N = S(t) + I(t)$$\n",
    "$$\\frac{dR}{dt} = \\gamma I$$\n",
    "\n",
    "$$R_{0} = \\frac{\\beta}{\\gamma}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import torch\n",
    "import matplotlib.pyplot as plt\n",
    "from deepchem.utils.differentiation_utils.integrate.explicit_rk import rk4_ivp\n",
    "\n",
    "def sim(t, y, params):\n",
    "    S, I = y\n",
    "\n",
    "    N = S + I\n",
    "\n",
    "    beta, gamma = params\n",
    "\n",
    "    dSdt = - beta * I * S / N + gamma * I\n",
    "    dIdt = beta * I * S / N - gamma * I\n",
    "\n",
    "    return torch.tensor([[dSdt], [dIdt]])\n",
    "\n",
    "t = torch.linspace(0, 500, 1000)\n",
    "\n",
    "beta = 0.04\n",
    "gamma = 0.01\n",
    "\n",
    "params = torch.tensor([beta, gamma])\n",
    "\n",
    "y0 = torch.tensor([[100], [1]])\n",
    "\n",
    "y = rk4_ivp(sim, y0, t, params).squeeze()\n",
    "\n",
    "plt.plot(t, y)\n",
    "plt.legend([\"Susceptible\", \"Infectious\"])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## References\n",
    "\n",
    "1. More Computational Biology and Python by Mike Saint-Antoine https://www.youtube.com/playlist?list=PLWVKUEZ25V97W2qS7faggHrv5gdhPcgjq\n",
    "\n",
    "2. Compartmental models in epidemiology. (2024, May 27). In Wikipedia. https://en.wikipedia.org/wiki/Compartmental_models_in_epidemiology\n",
    "\n",
    "3. Runge–Kutta methods. (2024, June 1). In Wikipedia. https://en.wikipedia.org/wiki/Runge%E2%80%93Kutta_methods"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Citing This Tutorial\n",
    "\n",
    "If you found this tutorial useful please consider citing it using the provided BibTeX.\n",
    "\n",
    "```bibtex\n",
    "@manual{Differential Equation, \n",
    " title={Differentiation Infrastructure in Deepchem}, \n",
    " organization={DeepChem},\n",
    " author={Singh, Rakshit kr. and Ramsundar, Bharath},\n",
    " howpublished = {\\url{https://github.com/deepchem/deepchem/blob/master/examples/tutorials/ODE_Solving.ipynb}}, \n",
    " year={2024}, \n",
    "} \n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Congratulations! Time to join the Community!\n",
    "\n",
    "Congratulations on completing this tutorial notebook! If you enjoyed working through the tutorial, and want to continue working with DeepChem, we encourage you to finish the rest of the tutorials in this series. You can also help the DeepChem community in the following ways:\n",
    "\n",
    "## Star DeepChem on [GitHub](https://github.com/deepchem/deepchem)\n",
    "This helps build awareness of the DeepChem project and the tools for open source drug discovery that we're trying to build.\n",
    "\n",
    "\n",
    "## Join the DeepChem Discord\n",
    "The DeepChem [Discord](https://discord.gg/SxSzjRRDMA) hosts a number of scientists, developers, and enthusiasts interested in deep learning for the life sciences. Join the conversation!"
   ]
  }
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